Chemical Thermodynamics | General Chemistry 3

Spontaneous process: a process that takes place without the input of energy from an external source
It generally leads to a decrease in the energy of the system ⇒ a spontaneous process is very often exothermic. But it's not always the case
 

2 H₂ (g) + O₂ (g) → 2 H₂O (l) is a spontaneous process
ΔH⁰_rxn = - 571.6 kJ.mol^-1 < 0 ⇒ exothermic reaction

H₂O (s) → H₂O (l) is a spontaneous process at T > 0°C
ΔH⁰_fus = +6.0 kJ.mol^-1 > 0 ⇒ not exothermic reaction

First Law of Thermodynamics:

The energy of the universe is constant ⇒ energy can neither be created nor destroyed
ΔU_univ = ΔU_sys + ΔU_surr = 0
⇒ ΔU_sys = - ΔU_surr = q + w

Second Law of Thermodynamics:

The total entropy of an isolated system can never decrease over time and is constant if all processes are reversible
⇒ the entropy change is never negative: ΔS_system + ΔS_surrounding $\ge$ 0
(ΔS_system + ΔS_surrounding = 0 for an equilibrium)

Entropy S (in J.K^-1): measure of the amount of disorder in a system (ex: expansion of a gas into a vacuum)
 

Entropy change on fusion:

Entropy change on vaporization:

Standard entropy change ΔS⁰_rxn for a chemical reaction (in J.K^-1.mol^-1):
 

a A + b B → c C
ΔS⁰_rxn = c S⁰ [C] – a S⁰ [A] – b S⁰ [B]

N₂ (g) + 3 H₂ (g) $\rightleftharpoons$ 2 NH₃ (g) 
ΔS⁰_rxn = 2 S⁰ [NH₃] – S⁰ [N₂] – 3 S⁰ [H₂]

Gibbs energy change ΔG_rxn (in J.mol^-1):
 

Gibbs criteria for reaction spontaneity:

• If ΔG_rxn < 0: reaction is spontaneous and additional products can form
• If ΔG_rxn > 0: reaction is not spontaneous ⇒ Input of energy from an external source is necessary to form additional products
• If ΔG_rxn = 0: reaction is at equilibrium

If Q > K  $\iff$  ΔG_rxn > 0: reaction proceeds spontaneously from right to left
If Q < K   $\iff$   ΔG_rxn < 0: reaction proceeds spontaneously from left to right
If Q = K   $\iff$   ΔG_rxn = 0: reaction is at equilibrium 
A reversible chemical reaction has reached equilibrium when the Gibbs free energy G_rxn reaches a minimum

Standard Gibbs energy change ΔG⁰_rxn for a reaction (in J.mol^-1):
 

ΔG_rxn = RT ln $\left(\frac{\mathrm{Q}}{\mathrm{K}}\right)$ = RT ln Q – RT ln K:
 

Standard Gibbs energy ΔG⁰_rxn for a chemical reaction (in J.mol^-1):
 

a A + b B → c C
ΔG⁰_rxn = c ΔG⁰_f [C] – a ΔG⁰_f [A] – b ΔG⁰_f [B]

N₂ (g) + 3 H₂ (g) $\rightleftharpoons$ 2 NH₃ (g)
ΔG⁰_rxn = 2 ΔG⁰_f [NH₃] – ΔG⁰_f [N₂] – 3 ΔG⁰_f [H₂]

ΔG⁰_rxn = ΔH⁰_rxn – TΔS⁰_rxn and ΔG⁰_rxn = - RT ln K

⇒ ln K = - $\frac{∆{{\mathrm{H}}^0}_{\mathrm{rxn}}}{\mathrm{RT}}$ + $\frac{∆{{\mathrm{S}}^0}_{\mathrm{rxn}}}{\mathrm{R}}$

⇒ a plot of ln K versus $\frac{1}{\mathrm{T}}$ is linear with slope - $\frac{∆{{\mathrm{H}}^0}_{\mathrm{rxn}}}{\mathrm{R}}$ and intercept $\frac{∆{{\mathrm{S}}^0}_{\mathrm{rxn}}}{\mathrm{R}}$

van’t Hoff Equation:
 

Clapeyron-Clausius Equation: